[JEE Advanced 1980] both roots of x b x c x a x c x a x
Both roots of $(x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0$ are always
(a) positive
(b) real
(c) negative
(d) none of these
1 Answer
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· 2d ago
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Correct answer: (b) real
It is $3x^2-2(a+b+c)x+(ab+bc+ca)=0$ with discriminant $2[(a-b)^2+(b-c)^2+(c-a)^2]\ge0$, so the roots are always real.
JEE Advanced 1980 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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